标题： 环谱的同伦理论，10年后 显示英文标题

标题： The homotopy theory of cyclotomic spectra, 10 years later

摘要： 本文研究了乘法等变稳定同伦理论中几何固定点函子的基础。 我们引入了一类称为广义轨道去悬架谱的等变正交谱，并分析了它们在几何固定点函子下的同伦行为，特别是与张量积和对称幂的相互作用。 这种分析导致了几项新的基础结果，包括在等变交换环正交谱上构造几何固定点的导出函子，并将其与在底层等变正交谱上的导出函子进行比较。 此外，该理论为交换环预循环谱范畴提供了基础，并给出了该范畴中映射导出空间的公式（作者与Yuan在相对TC论文中需要的公式）。 最后，我们证明了一个新的乘法Tom Dieck分裂，该分裂适用于作为非等变交换环谱的前推得到的等变交换环谱。 显示英文摘要

摘要： This paper studies the foundations of the geometric fixed point functor in multiplicative equivariant stable homotopy theory. We introduce a new class of equivariant orthogonal spectra called generalized orbit desuspension spectra and analyze their homotopical behavior with respect to the geometric fixed point functor and especially the interaction with smash products and symmetric powers. This analysis leads to several new foundational results, including the construction of the derived functor of geometric fixed points on equivariant commutative ring orthogonal spectra and its comparison to the derived functor on the underlying equivariant orthogonal spectra. In addition this theory provides foundations for the category of commutative ring pre-cyclotomic spectra and a formula for the derived space of maps in this category (a formula needed in the authors' paper with Yuan on relative TC). Finally, we prove a new multiplicative tom Dieck splitting for equivariant commutative ring spectra obtained as the pushforward of non-equivariant commutative ring spectra.